Abstract

It is a fundamental consequence of the superposition principle for quantum states
that there must exist nonorthogonal states, that is, states that, although different,
have a nonzero overlap. This finite overlap means that there is no way of determining
with certainty in which of two such states a given physical system has been prepared.
We review the various strategies that have been devised to discriminate optimally
between nonorthogonal states and some of the optical experiments that have been
performed to realize these.

K. Hunter, “Results in optimal
discrimination,” in Proceedings of The Seventh
International Conference on Quantum Communication, Measurement and Computing
(QCMC04), Vol. 734 of American Institute of
Physics Conference Series (AIP, 2004), pp.
83–86.

K. Hunter, “Results in optimal
discrimination,” in Proceedings of The Seventh
International Conference on Quantum Communication, Measurement and Computing
(QCMC04), Vol. 734 of American Institute of
Physics Conference Series (AIP, 2004), pp.
83–86.

K. Hunter, “Results in optimal
discrimination,” in Proceedings of The Seventh
International Conference on Quantum Communication, Measurement and Computing
(QCMC04), Vol. 734 of American Institute of
Physics Conference Series (AIP, 2004), pp.
83–86.

The support of a mixed state ρ̂ is the subspace spanned by its eigenvectors with nonzero
eigenvalues. The kernel of a mixed state is the subspace orthogonal to its
support.

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